2018-02-22T09:05:14Zhttp://toc.ui.ac.ir/?_action=export&rf=summon&issue=39432017-12-0110.22108Transactions on CombinatoricsTrans. Comb.2251-86572251-8657201764The central vertices and radius of the regular graph of ideals‎FarzadShaveisiThe regular graph of ideals of the commutative ring $R$‎, ‎denoted by ${Gamma_{reg}}(R)$‎, ‎is a graph whose vertex‎ ‎set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element‎. ‎In this paper‎, ‎it is proved that the radius of $Gamma_{reg}(R)$ equals $3$‎. ‎The central vertices of $Gamma_{reg}(R)$ are determined‎, ‎too‎.‎Arc‎‎artinian ring‎eccentricity‎‎radius‎‎regular digraph20171201113http://toc.ui.ac.ir/article_21472_57a7aea214c4516a524744b78f00943a.pdf2017-12-0110.22108Transactions on CombinatoricsTrans. Comb.2251-86572251-8657201764The harmonic index of subdivision graphsBibi NaimehOnagh‎The harmonic index of a graph $G$ is defined as the sum of the weights‎ ‎$frac{2}{deg_G(u)+deg_G(v)}$ of all edges $uv$‎ ‎of $G$‎, ‎where $deg_G(u)$ denotes the degree of a vertex $u$ in $G$‎. ‎In this paper‎, ‎we study the harmonic index of subdivision graphs‎, ‎$t$-subdivision graphs and also‎, ‎$S$-sum and $S_t$-sum of graphs‎.‎harmonic index‎‎subdivision‎‎$S$-sum‎‎inverse degree‎‎Zagreb index201712011527http://toc.ui.ac.ir/article_21471_6d4574ac2fe03052a0872fb991c96309.pdf2017-12-0110.22108Transactions on CombinatoricsTrans. Comb.2251-86572251-8657201764Splices, Links, and their Edge-Degree DistancesMahdiehAzariHojjatollahDivanpourThe edge-degree distance of a simple connected graph G is defined as the sum of the terms (d(e|G)+d(f|G))d(e,f|G) over all unordered pairs {e,f} of edges of G, where d(e|G) and d(e,f|G) denote the degree of the edge e in G and the distance between the edges e and f in G, respectively. In this paper, we study the behavior of two versions of the edge-degree distance under two graph products called splice and link.Distancedegreeedge-degree distancesplice of graphslink of graphs201712012942http://toc.ui.ac.ir/article_21614_033f4714ff9a47c358a450a46e9a3122.pdf2017-12-0110.22108Transactions on CombinatoricsTrans. Comb.2251-86572251-8657201764On the average eccentricity‎, ‎the harmonic index and the largest signless Laplacian eigenvalue of a graphHanyuanDengS.Balachandran‎S. K.AyyaswamyY. B.VenkatakrishnanThe eccentricity of a vertex is the maximum distance from it to‎ ‎another vertex and the average eccentricity $eccleft(Gright)$ of a‎ ‎graph $G$ is the mean value of eccentricities of all vertices of‎ ‎$G$‎. ‎The harmonic index $Hleft(Gright)$ of a graph $G$ is defined‎ ‎as the sum of $frac{2}{d_{i}+d_{j}}$ over all edges $v_{i}v_{j}$ of‎ ‎$G$‎, ‎where $d_{i}$ denotes the degree of a vertex $v_{i}$ in $G$‎. ‎In‎ ‎this paper‎, ‎we determine the unique tree with minimum average‎ ‎eccentricity among the set of trees with given number of pendent‎ ‎vertices and determine the unique tree with maximum average‎ ‎eccentricity among the set of $n$-vertex trees with two adjacent‎ ‎vertices of maximum degree $Delta$‎, ‎where $ngeq 2Delta$‎. ‎Also‎, ‎we‎ ‎give some relations between the average eccentricity‎, ‎the harmonic‎ ‎index and the largest signless Laplacian eigenvalue‎, ‎and strengthen‎ ‎a result on the Randi'{c} index and the largest signless Laplacian‎ ‎eigenvalue conjectured by Hansen and Lucas cite{hl}‎.‎Average eccentricity‎‎harmonic index‎‎signless‎ ‎Laplacian eigenvalue‎‎extremal value201712014350http://toc.ui.ac.ir/article_21470_6107bccf810358fdefb9471c7d0ba0a8.pdf2017-12-0110.22108Transactions on CombinatoricsTrans. Comb.2251-86572251-8657201764Some topological indices and graph propertiesXiaominZhuLihuaFengMinminLiuWeijunLiuYuqinHuIn this paper, by using the degree sequences of graphs, we present sufficient conditions for a graph to be Hamiltonian, traceable, Hamilton-connected or $k$-connected in light of numerous topological indices such as the eccentric connectivity index, the eccentric distance sum, the connective eccentricity index.Topological indicesdegree sequencesgraph properties201712015165http://toc.ui.ac.ir/article_21467_d05e2410fc3d5c5560f3430866b8af0e.pdf